Aircraft Lightning Certification using the FDTD Simulation Method

Lightning is just about the width of your thumb, but it can lead to fires, damage, and fried electronics. Lightning strikes an aircraft by lightning every 1,000 flight hours. This is why it is crucial for an aircraft to achieve lightning certification before it ever leaves the ground.

When lightning strikes an aircraft the lightning current flows along the surface of the aircraft. Lightning penetrates the inside of the body of the aircraft through electromagnetic (EM) fields generated by the strike. The resulting EM field is capable of inducing high voltages and current on the electrical cables which can lead to failures and/or compromise aircraft safety.

FAA lightning certification testing ensures that aircraft can avoid major damage from a strike by maintaining immunity levels. One can achieve this through either physical testing or simulation. Physical testing requires a model of the aircraft, which creates longer project timelines and drives up costs. Simulation  enables designers to change the design before a project enters production, and they can complete it before building a model.

Researchers use the finite-difference time-domain (FDTD) technique most for lightning simulations.

Understanding Lightning

Before you begin lightning certification, you need an understanding of how lightning forms and behaves.

Positive and negative charges fill the clouds with air acting as an insulator. Lightning occurs when the air breaks down due to a large difference in charges, causing a rapid discharge of electricity. You can see two types of lightning, cloud-to-cloud and cloud-to-ground, in Figure 1.

Fig. 1. Visual representation of charges in a cloud and lightning types.

In a typical cloud-to-ground strike, a channel of negative charges zigzag from the cloud to the ground following the path of least resistance, resulting in a forked pattern. A leader, an invisible column of charges, forms the path. As a downward leader heads toward the ground, taller objects send positive charges up creating an upward leader. An attachment point is where a downward leader and an upward leader meet. Changes in the electric field from previous lightning flashes can create additional upward leaders. Where an attachment point takes place depends on the height of the leaders and makes a significant difference to the waveform and amplitude of the current experienced by an aircraft in the lightning path.

Determining Waveforms

During the lightning certification and simulation process, differing waveforms and levels highlight the need to standardize lightning events. Standardized waveforms typically represent the worst-case scenario and include important characteristics of natural lightning flashes.

This simulation looks at the indirect effects of lightning. Indirect effects involve the voltage and current transients generated in aircraft wiring which can upset and/or damage components within electrical or electronic systems. Rates of current rise and decay and peak amplitude are the most relevant parameters when evaluating indirect effects of lightning.

Applicable waveforms (WF) for indirect effects are show in Figure 2 and include:

• WF H: A multiple burst consisting of a double exponential with 10 kA peak current and around 245 ns rise time. It represents one component of the current pulses that the leader development induces on an airframe conductive structure.
• WF A: The current pulse of a severe first return stroke and consists of a double exponential with 200 kA peak current and around 6.4 µs rise time.
• WF D: The current pulse of subsequent return strokes and consists of a double exponential with 100 kA peak current and around 3.2 µs rise time.

Fig. 2. Waveforms applicable to indirect effects of lightning simulations.

Indirect Effects of Lightning Certification

Lightning zoning is the process of dividing the aircraft into sections based on the probabilty of initial lightning flash attachment. Locations of zones depend on several factors including aircraft geometry and materials but also variables like altitude and velocity.

Designers analyze each zone with a major likelihood of lightning strike attachment by establishing the external EM environment. Waveforms A and H are applicable for zones with a high probability of initial lightning flash attachment, either for entry or exit. Designers study WF D in zones where they do not expect a severe initial return stroke, WF A. This helps identify the systems whose failure would prevent or reduce the capability of the aircraft to make a safe landing. Figure 3 shows an example of lightning zoning on a C-295.

Fig. 3. C-295 lightning zoning.

After establishing zones, we need to calculate different levels either by test or simulation. The levels are:

• Actual transient level (ATL): Current and voltage waveforms and levels that are induced on the aircraft at the port of the cable networks.
• Transient control level (TCL): Maximum allowable level of transient current and voltage. The aircraft design process selects standardized waveforms and levels early on.
• Equipment transient design level (ETDL): Current and voltage value for which the equipment has demonstrated tolerance without damage or upset.
• Equipment transient susceptibility level (ETSL): Current and voltage which will result in damage or upset when applied to equipment.

The ATL should be lower than the TCL. The TCL must be lower than the ETDL. The ETDL must be lower than the ETSL (ATL < TCL < ETDL < ETSL). We incorporate margins to account for uncertainties like cable routing, quality of the binding, ageing, maintenance operations, techniques employed in the equipment qualification, etc. The difference between the ETDL and the TCL defines the margins.

Design Protections

Aircraft have design protections that keep induced voltages and currents lower than equipmnt threshold values. Main protections include:

• Adding foil meshes to nonmetal aerodynamic surfaces over critical equipment.
• Using metallic strips to conduct the lightning current in areas that cannot be metallically covered such as antenna radomes.
• Protecting cables with shields or over braids grounded at each end to reduce the induced transients. This is provided that the signal is not a low frequency which would result in a worse situation.
• Using surge protection devices to protect equipment.

Indirect Effects of Lightning Simulation

Maxwell Equations Implementation:

To simulate the indirect effects of a lightning strike, we use Maxwell equations to calculate the EM field and current distribution. We typically apply the FDTD method, which solves the coupled Maxwell’s curl equations for both the electric and magnetic field in time and space.

The simulation creates a mesh with two interweaved grids of Yee cells alternating between E and H fields. The FDTD method solves the equation by taking the central difference approximation for both the temporal and spatial derivatives. To calculate the E field, we use the surrounding H values, and to solve for the H field, we use the surrounding E values. We iterate the procedure over time until we reach a stable condition. We need cell sizes in the order of millimeters to have a reliable representation of the geometry.

Simulation Method:

The steps necessary to prepare the simulation model are:

1. Obtaining and simplifying the CAD of the aircraft. We intend to simplify the model without degrading the simulation results. The model should still include all the required details from the EM point of view.
2. The simplified CAD is imported into a cubic Cartesian mesher to generate the 3D mesh which will be introduced into the solver.
3. A time step must be identified in order for the finite difference model to work. It has an upper limit which is given by the Courant criterion.
4. The EM properties of materials must be included e.g. permittivity, permeability, or impedance. This is especially important for any pieces that touch where the current will flow from one area to another. Several material types can be used such a perfect electric conductor (PEC), lossy, thin layer, anisotropic, or frequency dependent.
5. Cables inside the aircraft must be added, shown in Figure 4. They can be modeled in one of two ways. In each case special care must be taken between the cables and the structure or it could lead to a short circuit along the cable route.
   1. If the radius of a cable is up to 1/10 the size of a cell, then a thin wire model can be used. These cables are modeled as a line with appropriate resistance, inductance, and/or capacitance properties.
   2. If the bundle is greater than 1/10 the size of a cell, a mesh of the cable must be used. Electrical properties associated with the mesh can also be set. When using this method, it is important to prevent any undesired connections between different cables.
      

      Fig. 4. C-295 simplified cockpit geometry with related wiring.

6. The system simulates a lightning path through an entry point and exit point, as seen in Figure 5. The entry point is where there is a high probability of lightning strike attachment while the exit is where lightning detachment is probable.
   

   Fig. 5. Example of lightning current path in C-295.

7. To prevent the electric and magnetic fields from reflecting back into the problem space, we need to absorb the boundry conditions. Different types of boundary conditions include PEC, perfect magnetic conductor (PMC), MUR, and perfectly matched layer (PML).
8. You can use different probe types to make required measurements. In lightning simulations, the probes most used measure the wire current, either current along a thin wire or current through large structures, or mesh cables. Users can also obtain plots that depict field components or currents. We used Ansys EMC Plus software to find the results shown in Figures 6 and 7.

Fig. 6. Surface currents on cockpit.

Fig. 7. Tangential electric field on aircraft section.

Actual Transient Level Calculation

We evaluate the currents on the cables and then calculate the voltage stressing equipments using this formula:

• i(t) is the calculated value of the induced current
• R is the transfer impedance, which is dominated by the constant resistance in the range below 1 MHz
• l is the length of the run
• L is the cable inductance

Waveforms Shapes

One also needs to consider the resistance and/or inductance of the connectors or shield groundings and the number of cables inside the protection. The resulting induced transient waveform will depend on the cable protections:

• WF1 follows the shape of the lightning current. It represents the shape of the current induced in a low impedance cable loop due to the A component of a lightning strike.
• In bare cables the induced current generally follows the lightning current and flows along the cable. This generates a potential difference between the ends because of the impedance per unit length of the cable. This voltage has the shape of the induced current derivative or the lightning current derivative, Figure 8. We call this WF2.
  

  Fig. 8. Voltage induced on C-295 Rudder Booster Actuator bare cable.

• WF3 is a damped sinusoidal wave that represents the EM resonances excited in the cables by the lightning current.
• For over braided or shielded cables, the current is induced at the protection. A potential difference between the ends of internal cables appears due to the transfer impedance of the protection. We know this voltage as WF4 and it has the same shape as the induced or lightning currents, as Figure 9 illustrates.
  

  Fig. 9. Voltage induced on C-295 Elevator Trim Actuator over braided cable.

• WF5 represents the diffusion effects of a delayed waveform for structures made of carbon fiber instead of metallic structures.

We can use the same procedure to calculate the currents and voltages induced on the power plant, noise landing gear, main landing gear, and horizontal stabilizer.

Earning Lightning Certification

One FDTD simulation tool used to certify aircraft for indirect effects of lightning is Ansys EMC Plus. Developed by EMA, EMC Plus is a proven method of achieving certification through simulation. Built for cales and complex platforms, EMC Plus combines several numerical methods including FDTD, multi-conductor transmission line, and a transient circuit solver. EMC Plus is able to calculate all of the 3D coupling effects down to the individual pin and cable without the overhead other tools require.

EMA has decades of experience in indirect effects of lightning certification, allowing us to assess designs faster and more accurately. EMA’s approach to these problems leads to significant cost savings compared to test only approaches by reducing the risk of costly re-designs and testing/certification problems. SAE AC 20-136B and SAE ARP5415 accept EMA’s approaches as Methods of Compliance.

EMA can develop cohesive and efficient test plans and procedures, assess any issues related to test data, and conduct testing if required. This includes levels that are too high and data concerns. An EMA FAA Lighting Designated Engineering Representative (DER) aids in this process.

Learn more about our lightning certification services by clicking here.

EMA maintains EMC Plus and releases new features two times a year. Ansys sells the software exclusively. For more information click here.

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